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SOME CHARACTERIZATIONS OF HARDY SPACES ASSOCIATED WITH TWISTED CONVOLUTION

  • JIZHENG HUANG (a1)

Abstract

In this paper, we shall give some characterizations of the Hardy space associated with twisted convolution, including Lusin area integral, Littlewood–Paley g-function and heat maximal function.

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Copyright

Footnotes

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The author was supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 2007001040).

Footnotes

References

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[1] Anderson, R. F., ‘The multiplicative Weyl functional calculus’, J. Funct. Anal. 9 (1972), 423440.
[2] Auscher, P. and Russ, E., ‘Hardy spaces and divergence operators on strongly Lipschitz domains of ℝn’, J. Funct. Anal. 201 (2003), 148184.
[3] Coifman, R. R., Meyer, Y. and Stein, E. M., ‘Some new function spaces and their applications to harmonic analysis’, J. Funct. Anal. 62 (1985), 304335.
[4] Fefferman, C. and Stein, E. M., ‘H p spaces of several variables’, Acta. Math. 129 (1972), 137193.
[5] Folland, G. B. and Stein, E. M., Hardy Spaces on Homogeneous Groups (Princeton University Press, Princeton, NJ, 1982).
[6] Garcia-Cuerva, J. and Rubio de Francia, J. L., Weighted Norm Inequalities and Related Topics, North-Holland Mathematics Studies, 116 (North-Holland, Amsterdam, 1985).
[7] Grassman, A., Loupias, G. and Stein, E. M., ‘An algebra of pseudo-differential operators and quantum mechanics in phase space’, Ann. Inst. Fourier (Grenoble) 18 (1969), 343368.
[8] Mauceri, G., Picardello, M. and Ricci, F., ‘A Hardy space associated with twisted convolution’, Adv. Math. 39 (1981), 270288.
[9] Peetre, J., ‘The Weyl transform and Laguerre polynomials’, Le Matematiche 27 (1972), 301323.
[10] Stein, E. M., Topics in Harmonic Analysis Related to the Littlewood–Paley Theory (Princeton University Press, Princeton, NJ, 1970).
[11] Thangavelu, S., Lectures on Hermite and Laguerre Expansions, Math. Notes, 42 (Princeton University Press, Princeton, NJ, 1993).
[12] Thangavelu, S., ‘Littlewood–Paley–Stein theory on ℂn and Weyl multipliers’, Rev. Mat. Iberoamericana 6 (1990), 7590.
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